of the Electrical Current. 389 



If by B and B t we simply understand the diminution in the 

 consumption of zinc, we have with similar batteries 



A:A K ^B:B.p 



5. The vis viva which after the impact of two bodies a and b 

 is present in them is divided in the ratio of their masses. Hence 

 analogy would seem to indicate that quantities of heat disengaged 

 in the motor and in the conductor would bear the ratio / : \. This 

 conclusion corresponds to and confirms Joule's law. It has only 

 been experimentally demonstrated with certainty in the case of 

 solid conductors ; so that a length of wire of the resistance p 

 always developes the heat pV 2 . It is, on the other hand, most 

 probable that the law also applies to the motor ; but it has not 

 yet been confirmed experimentally. So far, therefore, there 

 is no proper proof, but only grounds of probability : and the 

 above analogy may be considered a further reason for proba- 

 bility; it is certainly not purely accidental.' 



6. If Joule's law be considered universally valid, we must ex- 

 pect for the developments of heat in the motor and conductor, 

 as for the vires vivce of two bodies impinging against each other, 

 similar relations, similar maxima and minima. As the agree- 

 ment cannot really be doubtful, it will be sufficient to confine 

 myself to the disengagement of heat in the motor and conductor. 



The magnitude of the vis viva depends in similar batteries only 



on the consumption of zinc, in dissimilar ones also on the factor — . 



As this factor may in each case be readily added, similar batteries 

 may be presupposed in the following. 



In a single cell the vis viva is divided over the motor and con- 

 ductor in the ratio I :\; in a cell with m times as large a sur- 

 face, in the ratio — : \. Hence by increasing the plates the vis 



viva is, as it were, taken out of the motor and transferred to the 

 conductor, while by increasing the cells it chiefly accumulates 

 in the motor. The greatest utilization of the heat, since it 

 must take place in the conductor, is only attainable by an in- 

 crease in the surface of the plates, or by increasing the resist- 

 ance; yet in the latter case it may be connected with a simulta- 

 neous decrease of the vis viva and of the consumption of zinc. 



If a battery be supposed unchanged, the conductor has its 

 maximum vis viva as soon as its resistance equals that of the 

 motor. On both sides of this resistance X lie corresponding 

 values \ + # and \—y, for which the vis viva is the same but 

 the consumption of zinc different. It is therefore possible that 

 with a smaller consumption of zinc a long wire might present 

 the same appearance of ignition as is produced by a greater con- 



